Question

# A sphere and a cone have the same volume, and each has a radius of 6 centimeters. What is the height of the cone?

Solid Geometry
A sphere and a cone have the same volume, and each has a radius of 6 centimeters. What is the height of the cone?

Equate the volumes of the sphere and the cone: Vsphere=Vcone $$\displaystyle\frac{{4}}{{3}}π{r}^{{3}}=\frac{{1}}{{3}}π{r}^{{3}}$$
$$\displaystyle\frac{{4}}{{3}}π{\left({6}\right)}^{{3}}=\frac{{1}}{{3}}π{\left({6}\right)}^{{2}}{h}$$
$$\displaystyle{288}π={12}π{h}$$